Implicit gradient-enhanced force-based Timoshenko fiber element formulation for reinforced concrete structures

In this paper, an implicit gradient force-based beam element is developed for analysis of reinforced concrete structures. The element is settled on the framework of Timoshenko beam theory, and adopts force interpolations to construct the element formulation. The sectional constitutive relation is described by the well-known fiber model, where the multi-axial softened damage-plasticity model is used for concrete fibers and the uniaxial Menegotto-Pinto model is used for steel fibers, thus the axial-flexure-shear interaction can be reflected naturally at material level. Furthermore, to overcome the localization issues arisen from strain-softening responses, the implicit gradient theory is introduced to the element. The weak form of the gradient enhancement is derived and an efficient subscale numerical solution is developed. The implementation of the proposed element is discussed in detail. Finally, a series of illustrative numerical examples are utilized to demonstrate the performance of the proposed element, and the results indicate that the element is able to reproduce accurate and objective responses of reinforced concrete structures under monotonic and cyclic loadings.